The double kicked top (DKT) is studied as an extension of the standard quantum kicked top (QKT) model. The model allows us to study the transition from time-reversal symmetric to broken time-reversal symmetric dynamics. A transformation in the kick strength parameter space $(k,k^{\prime })\to (k_r,k_{\theta })$ reveals interesting features. The transformed kicked strength parameter $k_r$ drives a higher growth of chaos and is equivalent to the standard QKT, whereas $k_{\theta }$ leads to a weaker growth. Fixed points and their stability are analyzed both analytically and computationally by using the largest Lyapunov exponent and the Kolmogorov-Sinai entropy. Exact solutions are obtained for 2- to 4-qubit version of the DKT, including eigenvalues, eigenvectors, and entanglement dynamics. Criteria for periodicity of the entanglement dynamics is obtained. Quantum correlations are investigated in both deep quantum and semiclassical regime. Signatures of phase-space structure are numerically shown in the long-time averages of the quantum correlations. The homoclinic point and its associated state are also investigated within the semiclassical regime. Our model can be realised experimentally as an extension of the standard QKT.

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• Chaos
• Entanglement entropy
• Entanglement measures
• Entanglement production
• Collective dynamics
• Floquet systems
• Quantum many-body systems
• Exact solutions for many-body systems